With the significant advance of vehicle-to-everything (V2X) techniques, unsignalized intersection coordination has been widely recognized to facilitate the development of automated vehicles (AVs) for the intelligent transportation system. However, how to guarantee driving safety while improving the unsignalized intersection management efficiency is a challenging issue. In this article, we investigate the collision-free and efficient V2X-enabled AV scheduling problem at unsignalized intersections. First, by dividing the intersection zone into different collision sections (CSs), we formulate the intersection collision-free model into an absolute value programming (AVP) problem, which is proved to be NP-hard. We consider both nonplatoon and platoon traffic scenarios, and unlike previous algorithms, which require to control all the AVs at each scheduling step with computational intractability, our scheduling algorithm can assign a feasible time for each arriving AV with low complexity. Further, we propose an alternately iterative descent method (AIDM) to solve the AVP problem by assigning the optimal entering time for each arriving AV. Through extensive simulations with various traffic data generated by SUMO, we demonstrate that our proposed AIDM algorithm can significantly enhance the scheduling performance in terms of passing delay and scheduling throughput. Even though the AIDM algorithm achieves the same level of transportation performances with the state-of-the-art algorithm, it advances dramatically in computational complexity and communication overhead, which is easier to be implemented in practice.